A contractor drew this diagram to find the area of a right-triangular shaped patio.

The length of railing b is 104 feet. The measure of angle A is 28°.

What is the area of the patio rounded to the nearest square foot?

The cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.

To find the cost per pound of each type of meat, we can set up a system of equations based on the given information.

Let's denote the cost per pound of rib steak as 'x' and the cost per pound of hamburger meat as 'y'.

From the first statement, we know that:

2x + 6y = 12.30 ---(Equation 1)

From the second statement, we know that:

3x + 2y = 9.70 ---(Equation 2)

Now we can solve this system of equations to find the values of 'x' and 'y'.

Multiplying Equation 1 by 3 and Equation 2 by 2 to eliminate the 'x' term, we get:

6x + 18y = 36.90 ---(Equation 3)

6x + 4y = 19.40 ---(Equation 4)

Subtracting Equation 4 from Equation 3, we get:

14y = 17.50

Dividing both sides by 14, we find:

y = 1.25

Substituting the value of 'y' back into Equation 1, we can solve for 'x':

2x + 6(1.25) = 12.30

2x + 7.50 = 12.30

2x = 4.80

x = 2.40

Therefore, the cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.

for such more question on cost

https://brainly.com/question/8993267

#SPJ8

The value of x in the triangle ABC is 25.

The interior angles of the triangle are given as m∠A = 3x and m∠B = 50°.

The exterior angle of the triangle is given as m∠ACD = 5x.  

The sum of angle in a triangle is equals to 180 degrees. Therefore,

3x + 50 + (180 - 5x)  = 180

3x + 50 - 5x + 180 = 180

3x - 5x + 50 + 180 = 180

-2x + 230 = 180

subtract 230 from both sides

-2x + 230 - 230 = 180 - 230

-2x = -50

divide both sidesby -2

-2x / -2 = -50 / -2

x = 25

learn more on triangles here: https://brainly.com/question/27100907

Answer: 75%

Step-by-step explanation: 4+3+5=12. 12-3=9. So the probability of not picking orange is 9/12, or 3/4. 3/4=75%. So the answer would be 75%

The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

To solve more questions on inverse of function, visit the link below-

brainly.com/question/28229665

#SPJ1

A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

for such more question on overall flow

https://brainly.com/question/10922478

#SPJ11

x=2

hope this helped

The width RQ of the river is approximately 61.98 ft.

To find the width RQ of the river, we can use the properties of perpendicular lines and collinearity.

Given that Karl starts at point R and walks perpendicular along the edge of the river 42 ft to point S, we can draw a line segment RS of length 42 ft.

From point S, Karl walks 28 ft further to point T. We can draw another line segment ST of length 28 ft.

Now, Karl turns 90° from point T and walks until his location (point U), point S, and point Q are collinear. Let's denote the length of this line segment as UQ.

From the given information, we know that TU = 68 ft.

Since U, S, and Q are collinear, we can form a right triangle by connecting UQ and US.

The length of UQ can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

UQ² = TU² - US²

UQ² = 68² - 28²

UQ² = 4624 - 784

UQ² = 3840

Taking the square root of both sides, we have:

UQ = √3840

UQ ≈ 61.98 ft

Therefore, the width RQ of the river is approximately 61.98 ft.

Note: It's important to keep in mind that this solution assumes the river is a straight line and that Karl's path is perpendicular to the river's edge. In reality, the river's edge may not be perfectly straight, and the path Karl walks may not be exactly perpendicular.

For more such questions on width visit:

https://brainly.com/question/25292087

#SPJ8

Answer:

Step-by-step explanation: I had $37 in my bank account but my monthly fee for PlayStation plus Internet connection is $40 so my bank account  Got drafted 3 dollars that I didn’t have So now I have -3 dollars

The slope of the line is 4.83 and the y-intercept is 51

From the graph, we can see that the line of the best fit touches the y-axis at y = 51

This means that:

The y-intercept is 51

The slope is then calculated as:

m = (y2 - y1)/(x2 - x1)

Using the points on the line, we have:

m = (80 - 51)/(6 - 0)

Evaluate

m = 4.83

Hence, the slope of the line is 4.83

Read more about line of best fit at:

https://brainly.com/question/25226042

#SPJ1

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

Using the coordinates of the vertices of a polygon (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1) the perimeter of the polygon is 16.0 units

The perimeter is calculated by summing the sides

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

(-3, 1) and (-3, 3) =√{(-3 - -3)² + (3 - 1)²} = 2

(-3, 3) and (-1, 5) = √{(-1 - -3)² + (5 - 3)²} = 2√2

(-1, 5) and (2, 4) = √{(2 - -1)² + (4 - 5)²} = √10

(2, 4) and (2, 1) = √{(2 - 2)² + (1 - 4)²} = 3

(2, 1) and (-3, 1) = √{(-3 - 2)² + (1 - 1)²} = 5

The perimeter = 2 + 2√2 + √10 + 3 + 5

The perimeter = 15.9907

The perimeter = 16.0 units

Learn more about length of line segment  here:

https://brainly.com/question/24778489

#SPJ1

Answer:

k = 4

Step-by-step explanation:

Given polynomial is,

kx² - 12x + 9

We have to find the value of 'k' for which the given polynomial is a square of a binomial.

To find this we will use the formula,

(a - b)² = a² - 2ab + b²

kx² - 12x + 9 = kx² - 2(6x) + 3²

                    = kx² - 2(3)(2x) + 3²

By comparing this with the formula of (a - b)²,

b = 3

a = 2x

(2x)²- 2(2x)(3) + 3² = (2x - 3)²

4x² - 12x + 9 = (2x - 3)²

Therefore, k = 4 will make the polynomial a perfect square of a binomial.

The surface area of the complex solid is 530 square yards.

In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:

A = w · h

Where:

The surface area of the complex solid is:

A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)

A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²

A = 530 yd²

To learn more on surface areas of solids: https://brainly.com/question/31126484

#SPJ1

Answer:

Step-by-step explanation:

Let's start by finding the fraction of the garden that George weeded. We know that he weeded 1/5 of the garden, so the fraction that is left is:

1 - 1/5 = 4/5

Now we know that Summer weeded enough to leave 2/3 of the garden still needing to be weeded. This means that she weeded:

1 - 2/3 = 1/3

of the garden.

However, we want to find the fraction of the garden that Summer weeded relative to the total garden, not just the part that was left after George weeded. So we need to express this fraction as a fraction of the total garden.

To do this, we can use the fact that George weeded 1/5 of the garden, or equivalently, 5/5 + 1/5 = 6/5 of the garden. So the total garden is divided into 6 equal parts, each representing 1/5 of the garden.

Since George weeded 1/5 of the garden, there are 5/5 - 1/5 = 4/5 parts of the garden left. This means that 4/5 of the garden is divided into 3 equal parts, each representing 1/3 of the garden (since Summer left 2/3 of the garden to be weeded).

Therefore, the fraction of the garden that Summer weeded is:

1/3 * (4/5) = 4/15

So Summer weeded 4/15 of the garden.

The length of the hypotenuse of the sail is 18.30 feet long.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

a² + b² = c²

Given that the sail for his sailboat is a 45-45-90 Right Triangle. 15. The base of the sail is 10.5 ft. long.

a² + b² = c²

Therefore,

15² + 10.5² = c²

c² = 15² + 10.5²

c² = 225 + 110.25

c² = 335.25

c = 18.30

Thus, the hypotenuse is 18.30 feet long.

Learn more about Pythagoras theorem;

https://brainly.com/question/343682

#SPJ2

The transformed equation of \(y = x^{3}\) is \(y = -\frac{1}{7} (x + 8)^{3}\).

Given equation ;  \(y = x^{3}\)

Applying the given transformations, we have:

To have a vertical compression by a factor of  \(\frac{1}{7}\), we need to multiply the function by  \(\frac{1}{7}\). So, we have:

\(y =\)  \(\frac{1}{7}\) \(x^{3}\)

To have a horizontal shift by 8 units to the left, we need to add 8 to x. So, we have:

\(y = \frac{1}{7} (x + 8)^{3}\).

Lastly, to have a reflection over the x-axis, we need to multiply the function by −1. So, we have:

\(y = -\frac{1}{7} (x + 8)^{3}\).

Therefore, the transformed equation is  \(y = -\frac{1}{7} (x + 8)^{3}\).

Learn more about transformation here;

https://brainly.com/question/2689696

#SPJ4

Answer:

105

Step-by-step explanation:

its said that you used 7 tablespoons for 4 tablespoons for baking soda so i did 15X7 and that get you 105

The amount of usage of vinegar is 26 \(\frac{1}{4}\) (26.25) tablespoons.

Calculations :

             produce a chemical reaction with

              7 tablespoons of vinegar                       =  4

              So , divide both :  15/4 = 3.75 = 3 3/4

                                          = 3.75 x 7 = 26.25 = 26 1/4 tablespoons

                                                                                          of vinegar

Learn more about Recipe conversion factor refer :

https://brainly.com/question/28319558

#SPJ2

Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be congruent if all the three angles and three sides of one triangle is equal to the three sides and three angles of the other triangle.

Statement                             Reason

RS ⊥ TS and RV ⊥ TV           Given

∠S = ∠V are right angles      Definition of perpendicular. Since RS ⊥ TS,

                                               hence ∠S = 90° and RV ⊥ TV hence ∠V = 90°

ST ≅ VT                                  Given

RT ≅ RT                                  Reflexive property of congruence

ΔTSR  ≅ ΔTVR                      Hypotenuse leg congruence theorem. For

                                              two right triangles, if the hypotenuse and leg

                                              of one triangle is the same as the hypotenuse

                                              and leg of the second triangle, then the two

                                               triangles are congruent.

RS ≅ RV                                  Definition of congruency.

9514 1404 393

Answer:

  $11,680.58

Step-by-step explanation:

Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.

__

The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.

The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...

  0.205×21,465 = 4400.325 ≈ 4400.33

The the total tax due on $70,000 is ...

  $7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000

_____

Additional comments

The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.

__

Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.

  ≤ 48535 -- income × 0.15

  ≤ 97069 -- income × 0.205 -2669.425

  ≤ 150,473 -- income × 0.26 -8008.22

  ≤ 214,368 -- income × 0.29 -12,522.41

  > 214,368 -- income × 0.33 -21,097.13

In this case, the second row of this simpler table would give the tax on $70,000 as ...

  tax = 70,000 × 0.205 -2669.425

  tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above

Answer:

Step-by-step explanation:

The  histogram shown in the attached file show that the distribution of differences is approximately normal.

So, we can assume that the distribution is normal.

.

b)

The 95% confidence level for \(\mu _D=\mu_1-\mu_2\) is found

\(\bar d \pm t_{0.025,11}\frac{S_D}{\sqrt{n} }\)

\(=0.666667 \pm 2.201\frac{(2.964436)}{\sqrt{12} } \\\\0.666667 \pm 2.201(0.85576)\\\\=0.666667+ 1.883525474=2.5502\\\\=0.666667- 1.883525474=-1.2169\\\\=(-1.2169,2.5502)\)

since 0  is in the confidence interval. we do not reject the null hypothesis.

No, there is no indication of one design language is available.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

y = -5x

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

5x+y = 0

Subtract 5x from each side

5x+y-5x= 0-5x

y = -5x

Answer:

33.0693394

Step-by-step explanation:

1 klio is 2.20462262,just mulipily by 15.

Answer:

first option

imagine the line y = x as a mirror

Answer:

The answer is A. "the function h because the graphs of ƒ and h are symmetrical about the line y = x"

Answer:

\(\frac{2\pi }{3} \ ,\ \pi \ ,\ \frac{4\pi }{3}\)

Step-by-step explanation:

suppose cos(x) = y

Then

\(2\cos^{2} \left( x\right) +3\cos x+1=0\Longleftrightarrow \begin{cases}2y^{2}+3y+1=0&\\ y=\cos \left( x\right) \ \ \text{and} &0\leqslant x\leqslant 2\pi \end{cases}\)

2y² + 3y + 1 = 0 ⇒ y = -1 or y = -1/2  (because 2-3+1=0)

y = -1 ⇔ cosx = -1 ⇒ x = π  (because x∈[0,2π] )

y = -1/2 ⇔ cosx = -1/2 ⇒ x = 2π/3 or x = 4π/3

Final answer :

x = π or x = 2π/3 or x = 4π/3

a. Apples:  Lily needs 10 cups of apples for her fruit bowl.

b. Watermelons: Lily needs 13-3/4 cups of watermelons for her fruit bowl.

c. Grapes: The amount of grapes that Lily has is not given

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To make her fruit bowl, Lily needs 2½ times the amount of each fruit she currently has.

a. Apples:

2½ × 4 cups = 10 cups

Therefore, Lily needs 10 cups of apples for her fruit bowl.

b. Watermelons:

2½ × 5-½ cups = (2 × 5 + 1/2) × 5/2 cups = 13-3/4 cups

Therefore, Lily needs 13-3/4 cups of watermelons for her fruit bowl.

c. Grapes:

The amount of grapes that Lily has is not given, so we cannot calculate how much she needs for her fruit bowl.

To learn more about arithmetic sequence from the given link:

https://brainly.com/question/15412619

#SPJ1